I've had dealers swap a plate from a trade-in over to a car I was purchasing.
I've done this on a trade-in against a brand new car, and on a trade-in against a "nearly new".
The brand-new car was obviously first registered with the personalised plate. As such, I drove to the dealer with my trade-in (displaying my personal plate) and drove away with the new car (also displaying my personal plate).
This is probably not technically legal - although I suspect (given the REAMS of paperwork I had on me on both journeys), the police would have to have been VERY bored to pursue a prosecution.
The various dealers have always done the paperwork quickly and efficiently, and charged me no more than I would have had to pay directly to the DVLA had I done the change myself.
In fact, you want to be able to transfer the plate to the new car directly. By placing the plate on retention (instead of transferring directly), I believe it costs you slightly more in the long run.
Lee RS would be better suited to answer this question - he's bought more plates than I've had hot dinners....
I suspect the dealer concerned in this case simply doesn't want to be bothered with the paperwork chore - or is unsure of the procedure himself. Given the dealers reluctance to do it, I would be inclined to not press the point and do it myself. At least then you know it's been done correctly. The potential for "losing" the plate is ever present - you don't want the dealers apathy to be the cause of you losing your personal plate.